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Saturday, March 15, 2014

Guest Post: An Open Letter to Sean Carroll

Today's post is by Guest Author Jack Spell.

Dr. Carroll,

I want to thank
you again for all of the thought-provoking material you produced over the two
days of the conference. I say “again” because I was fortunate enough to have
the opportunity to thank you in person on Saturday after the conference had
concluded. You might remember me; I was the really conspicuously good-looking
guy who, during the Q & A on Friday and Saturday, asked you about (1) an
eternal set of necessary and sufficient mechanical conditions producing a
universe containing a first moment of time, and (2) the specifics of Alan
Guth’s affirmation of the probable eternality of the universe, respectively.
Alright, alright, I may have exaggerated the part about my good-looks a little,
but in all seriousness you might possibly remember the questions. Nevertheless,
it was a real privilege to shake your hand and I thoroughly enjoyed hearing
your take on these interesting issues. Having familiarized myself with some of
your published work, I’m well aware that you are skilled writer. But having
never seen you lecture or debate, I had no idea that you would prove to be such
a wonderful public speaker and formidable debater. I look forward to more of it
in the future.

While I’m sure
that you have entirely too much on your plate to respond to every reply on your
blog, nevertheless I would owe you a great debt of gratitude if you’re able to
somehow find the time to respond to this one; that is, provided it’s
substantive enough to warrant a response.

In light of a
recent post, you seemed to have cleared up what led to a persistent confusion
for some during the debate: namely, your maintaining that a universe with a
“first moment of time” isn’t necessarily one that “begins to exist.” It seems
to me that you are able to consistently hold to this view because you ascribe
to a tenseless or, B-Theory, of time. That is what I suspected. So if I
understand you correctly, are you saying that a universe with a first moment of
time doesn’t “begin to exist” because, on the B-Theory, the entire universe
exists *timelessly* for all eternity as a static, 4-dimensional block? If so,
is it not perfectly legitimate to inquire as to what determines that this
particular statically-existing universe obtains, rather than some other one or
none at all? Also, would you agree that the A-Theory of time is the much more
common sense view?

Moreover, there
appears to be a few points in your post-debate reflections that might be cause
for reflection. First, regarding your denial of both the premises in the Kalam
Cosmological Argument (KCA), you said,

“My attitude
toward the above two premises is that (2) is completely uncertain, while the
“obvious” one (1) is flat-out false. Or not even false, as I put it, because
the notion of a “cause” isn’t part of an appropriate vocabulary to use for discussing
fundamental physics.”

As WLC has
repeatedly emphasized, he does not claim anything near “certainty” for the
truth of these premises. Rather, he merely defends the notion that they are
more plausibly true than their negations; the greater the degree to which they
are more plausibly true than not, the stronger the argument becomes. So while I
agree that we don’t have certainty with respect to the truth of premise (2), I
do believe that we have good reason to believe that it is much more plausibly true
than not; which is what a good argument entails.

With respect to
the notion of a “cause,” I would have to disagree with your thinking that this
isn’t the appropriate vocabulary to use here. The univocal meaning employed in
KCA is “that which produces the effect.” Thus, if we were to ask, “What is the
’cause’ of virtual particles?”, we would be asking, “What ‘produces’ virtual
particles?”, with the answer to which — quantum fluctuations in the vacuum —
being completely legitimate. Similarly we could ask, “What is the ’cause’ of
the binding of like-charged nucleons in the atomic nucleus?”, and someone would
answer, “The strong force is what produces that effect.” So it seems to me that
a clear definition of terms makes appropriate the use of a “cause” in this
context.

With that being
said, when you say that, “The Hartle-Hawking ‘no-boundary proposal’ for the
wave function of the universe, for example, is completely self-contained, not
requiring any external cause,” in what sense do you mean, “self-contained?” It
was pointed out in [http://arxiv.org/abs/astro-ph/9712344] that,

“The problem
with this model is that it ignores the “zero-point-energy”. . . . Thus, when
the “zero-point-energy” is considered, we see that the initial state is not a
point but a tiny oscillating (0 ≤ a ≤ a1) Big Bang universe, that oscillates
between Big Bangs and Big Crunches (though the singularities at the Big Bangs
and Big Crunches might be smeared by quantum effects). This is the initial
classical state from which the tunneling occurs. It is metastable, so this
oscillating universe could not have existed forever: after a finite half-life,
it is likely to decay.”

Therefore it
seems to me that on this model the universe has only existed for a finite
duration of time. So we could still validly inquire as to what produced it (Or,
given the more radical B-Theory of time, what determined that *this* universe
tenselessly exists rather than some other). Moreover, why think that this model
shouldn’t be treated as nonrealist in character? How does changing from a
Lorentzian metric signature to a Euclidean metric imply an ontological
commitment? Given the fact that the Wick rotation performed takes the real time
variable “T” and replaces it with the imaginary quantity “I × T”, Hartle and Hawking
are said to employ “imaginary time” in their model. How does one intelligibly
give a realistic interpretation to any value of “imaginary time?”

You later go on
to state the following:

“The second
premise of the Kalam argument is that the universe began to exist. Which may
even be true! But we certainly don’t know, or even have strong reasons to think
one way or the other. Craig thinks we do have a strong reason, the
Borde-Guth-Vilenkin theorem. So I explained what every physicist who has
thought about the issue understands: that the real world is governed by quantum
mechanics, and the BGV theorem assumes a classical spacetime, so it says
nothing definitive about what actually happens in the universe; it is only a
guideline to when our classical description breaks down.”

It goes without
saying that I would never claim to be any kind of subject matter expert on
cosmology, especially when in comparison with your current level of expertise.
However, in my novice opinion, I think it’s fair to say that last statement
downplays the significance of BVG and, as far as I can tell, is false. While I
agree that we can’t infer anything “definitive,” I think we can, however, make
some significant inferences: given the fact that we have *substantial* evidence
that our universe satisfies the only condition of BVG — Hav > 0 — all the
way back until 10^-43 seconds, then according to
[http://arxiv.org/abs/gr-qc/0110012],

“Whatever the
possibilities for the boundary, it is clear that unless the averaged expansion
condition can somehow be avoided for all past-directed geodesics, inflation
alone is not sufficient to provide a complete description of the Universe, and
some new physics is necessary in order to determine the correct conditions at
the boundary [20]. This is the chief result of our paper. The result depends on
just one assumption: the Hubble parameter H has a positive value when averaged
over the affine parameter of a past-directed null or noncomoving timelike
geodesic.

“The class of
cosmologies satisfying this assumption is

not limited to
inflating universes.”

Vilenkin
reiterates the point:

“A remarkable
thing about this theorem is its sweeping generality. We made no assumptions
about the material content of the universe. We did not even assume that gravity
is described by Einstein’s equations. So, if Einstein’s gravity requires some
modification, our conclusion will still hold. The only assumption that we made
was that the expansion rate of the universe never gets below some nonzero
value, no matter how small. This assumption should certainly be satisfied in
the inflating false vacuum. The conclusion is that past-eternal inflation
without a beginning is impossible.” [Vilenkin, Many Worlds in One, p. 175]

Thus, we have very
good reason to think that unless the Planck epoch can avoid Hav > 0, our
universe cannot be past-eternal. One possible way for this to happen is via an
“emergent universe” scenario. In discussing a model of this type, you mentioned
a paper by Anthony Aguirre and John Kehayias; one that WLC cited in the debate:

“They examined
the “emergent universe” scenario of George Ellis and Roy Maartens, in which the
universe is in a quasi-static pre-Big-Bang state infinitely far into the past.
Aguirre and Kehayias showed that such behavior is unstable; you can’t last in a
quasi-static state for half of eternity and then start evolving. Personally, I
didn’t think this was worth talking about; I completely agree that it’s
unstable, I never promoted or defended that particular model, and I just didn’t
see the relevance. But he kept bringing it up. Only after the debate did it
dawn on me that he takes the specific behavior of that model as representative
of any model that has a quantum-gravity regime (the easiest way out of the
“beginning” supposedly predicted by the BGV theorem). That’s completely false.
Most models with a quantum-gravity phase are nothing like the emergent
universe; typically the quantum part of the evolution is temporary, and is
surrounded on both sides by classical spacetime. But that’s so false that I
didn’t even pick up that WLC was presuming it, so I never responded. Bad
debater.”

According to
that paper [http://arxiv.org/abs/1306.3232],

“We stress that
we have analyzed only one version of the Emergent Universe, with a simplified
model. Nonetheless, we believe that the effect that this analysis points to may
be rather generic. For example, consider alternative theories of gravity. The
Emergent Universe has been studied extensively in theories such as
Hoˇrava-Lifshitz, f(R), Loop Quantum Gravity7, and others (see, for instance,
[8–11], respectively). There have also been several studies of the stability of
the Einstein static universe in alternative theories (see [12], for example).
However, in our framework we have, in a sense, decoupled gravity – it enters
only when assessing the affect of the spreading wave-functional. Even in
alternative theories in which the Einstein static universe is more stable than
in standard General Relativity, we anticipate that once the wavefunctional has
spread enough, the geometry must follow, and the spacetime becomes classically
ill-defined as well as containing portions corresponding to singularities.
Therefore, this seems like a generic (and perhaps expected, given our
construction of the scenario) problem with such an eternal and precisely tuned
inflationary scheme. . . .”

“. . . Models
in which the field dynamics and material content are very different would
require separate analysis, but may lead to a similar basic conclusion. For
example, Graham et al. [14] construct static and oscillating universes with a
specific non-perfect-fluid energy component that are stable against small
perturbations. However, Mithani & Vilenkin [15] have shown that this model
is unstable to decay via tunneling.

“Although we
have analyzed only one version of the Emergent Universe, we would argue that
our analysis is pointing to a more general problem: it is very difficult to
devise a system – especially a quantum one – that does nothing “forever,” then
evolves. A truly stationary or periodic quantum state, which would last
forever, would never evolve, whereas one with any instability will not endure
for an indefinite time.”

Unless I’m
missing something, this paper seems to strongly support WLC’s contention:
quantum instability seems to prevent *any* emergent scenario — regardless of if
it’s an unstable state (ESS) or a metastable state (LQG) — from being
past-eternal. Moreover, this notion appears to be reinforced here
[http://arxiv.org/abs/arXiv:1305.3836] as well:

“A number of
authors emphasized that the beginning of inflation does not have to be the
beginning of the universe. The ‘emergent universe’ scenario [11–15] assumes
that the universe approaches a static or oscillating regime in the asymptotic
past. In this case, the average expansion rate is Hav = 0, so the condition (1)
is violated. The problem with this scenario is that static or oscillating
universes are generally unstable with respect to quantum collapse and therefore
could not have survived for an infinite time before the onset of inflation
[16–18].”

I’m just not
following you here; what would lead you to say that this belief of WLC is
“completely false?”

With respect to
a model that posits a different scenario, you said,

“In contrast, I
wanted to talk about a model developed by Anthony Aguirre and Stephen Gratton.
They have a very simple and physically transparent model that (unlike my theory
with Chen) imposes a low-entropy boundary condition at a mid-universe “bounce.”
It’s a straightforward example of a perfectly well-defined theory that is
clearly eternal, one that doesn’t have a beginning, and does so without
invoking any hand-waving about quantum gravity. I challenged Craig to explain
why this wasn’t a sensible example of an eternal universe, one that was in
perfect accord with the BGV theorem, but he didn’t respond. It wasn’t until the
talks on the following day that Craig’s teammate James Sinclair admitted that
it seemed like a perfectly good model to him.”

Vilenkin also
addressed this model in the last paper I mentioned, and noted:

“Even though
the spacetime has no boundary in the AG model, it does include a hyper-surface
on which the low-entropy (vacuum) boundary condition must be enforced by some
mechanism. This surface of minimum entropy plays the role of the beginning of
the universe in this scenario. . . .”

“. . . Suppose
the vacuum that fills this de Sitter space is a metastable (false) vacuum and
that it can decay to one or more lower-energy vacua through bubble nucleation.
Suppose further that we impose a boundary condition that the entire universe is
in a false vacuum state in the asymptotic past, τ → −∞. Then bubbles nucleating
at τ → −∞ will fill the space, the energy in the bubble walls will thermalize,
and the universe will contract to a big crunch and will never get to the bounce
and to the expanding phase.”

Even if one
ignores the questionable reversal of the arrow of time, this model, according
to Vilenkin, still cannot plausibly be past-eternal.

Nevertheless,
this post is beyond lengthy already so I’ll stop here, despite my remaining
questions. As I said, thanks again for such a civil, competitive debate and I
appreciate your taking the time to entertain my questions.

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7 comments:

This is probably a dumb question (and I hope it makes sense), but I'll go ahead anyway: When scientists talk about what may have happened before the big bang, why is it they (or some of them anyway) talk of our universe coming out of a vacuum state as opposed to coming from another universe filled with matter much like our own? Why does it have to come from a vacuum?

So there is actually something you don't know after all :). The only thing I could come up with is that maybe they choose to have the universe come from a pre-existing vacuum because vacuums produce fluctuations and they are, theoretically, capable of producing a universe like ours, whereas maybe universes filled with matter like our own don't have this capability for some reason. Just a thought. Hope somebody else can help :)

Actually vacuum fluctuation models are just one of the asymptotically static cosmogonic scenarios purporting to describe what happened 'prior' to the Big Bang; there are also eternal inflationary models, cyclic models, contracting models, and other asymptotically static models. Like vacuum fluctuations models, these others are also plagued with problems and none of them, even if true, succeed in restoring past-completeness. Thanks for your question and I hope this helps.

Hmm...OK. I was aware of other models out there, but I'm just a little baffled as to why some feel a need to posit a vacuum at all? After all, I guess there's no way to scientifically prove a vacuum existed pre-universe (or is there?) so I can't see why they even posit it, apart from maybe what i said already about it producing fluctuations which theoretically might have the capability of creating a universe?. Hope that makes sense & thanks for the original answer anyhow :)

It seems to me that the primary motivation behind positing a primordial vacuum is simply to avoid the absolute beginning implied by the Standard Big Bang Model. Let me explain. We can say with virtual certainty that classical spacetime (i.e., our observable universe subsequent to 10^-43 seconds) has been in a state of cosmic expansion throughout its history -- as Vilenkin affirmed, *all* of the evidence we have suggests this. Moreover, the BVG Theorem [http://arxiv.org/abs/gr-qc/0110012] says that *any* spacetime that satisfies this sole condition cannot be geodesically past-complete (i.e., eternal). Thus, the primordial vacuum state is proposed as an attempt to evade the BVG Theorem by avoiding Hav > 0 due to there being an infinite amount of time spent in the vacuum state.

However, even if this scenario could in principle avoid BVG, it's not out of the woods yet; it still faces a deep internal incoherence: according to such models, it is impossible to specify precisely when and where a fluctuation will occur in the primordial vacuum which will then grow into a mini-universe. Within any *finite* interval of time there is some non-zero probability of such a fluctuation occurring at any point in space. Thus, given *infinite* past time, mini-universes will eventually be spawned at *every* point in the primordial vacuum, and, as they expand, they will begin to collide and coalesce with one another. Therefore, given infinite past time, we should by now be observing an infinitely old universe, not a relatively young one. As WLC stated in the debate, if the vacuum were sufficient to produce the universe, it would have done it infinitely-long-ago. As a last resort, one could posit an expansion in the vacuum itself so as to remedy this incoherence. After all, de Sitter spacetime is the exact solution of the Einstein equations Gµν + Λgµν = 0 for the empty universe with positive vacuum energy density. But then we're right back where we started! Namely, the universe, *including* the vacuum state, would satisfy Hav > 0 and therefore necessarily have a beginning.